24. Chromium

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Below: Electron Shell, Bonding & Ion Formation, Magnetic Properties, Electric Properties

Chromium is the 24^th element on the periodic table. It has 24 protons and 28 neutrons for a mass of 52 amu, and 24 electrons.

Electron Shell

DISCLAIMER: This electron domain geometry is designed to show the most symmetrical resonance structure for the orbitals, according to the Quicycle model. This is not the only resonance structure possible for this element. (In this series we are also not differentiating between high-spin and low-spin states. These variations should be extrapolated from the geometries shown.)

Chromium is the fourth element to feature electrons in the d–orbital. Building upon the pd-hybridization [ref] we introduced in regard to scandium (Sc), titanium (Ti), and vanadium (V), it is proposed that chromium has a 3^rd shell containing 3 di-electrons and 5 unpaired electrons in p³d⁵-hybridized, hexagonal bipyramidal symmetry. The three p-orbital di-electrons occupy three symmetrically distant equatorial positions to minimize repulsion. The 5 unpaired electrons occupy the remaining equatorial and axial positions. (See image below.)

This pd-hybridization does not need to involve the 3s-orbital electrons, which can remain in their preferred spherical di-electron state, within which (or upon which) the hybrid orbitals will resonate like harmonics upon a fundamental. However, the standard electron configuration shown below illustrates that one electron from the 4s-orbital joins the 3^rd shell hybridization. This model suggests that the reason for this is to achieve symmetry in eight directions, and to avoid the asymmetry of seven directions whenever possible. (Note that 7-directional electron geometry is possible, of course, via a pentagonal bipyramidal structure. The purpose of this page, however, is to show the most symmetrical, spherically-harmonic atomic resonance state, even if it is not the lowest possible energy state.)

In such a configuration, the 4 tetrahedral 2^nd shell di-electrons will align themselves with one di-electron opposite one of the single electrons in the 3^rd shell, allowing all other di-electrons to orient their directions roughly between one another in order to minimize repulsion between shells.

NOTE: The small spheres in the image above simply indicate the directions of maximum electron density. The 3^rd shell hybrid orbitals themselves will assume a spherical hexagonal bipyramidal structure that divides the 3^rd shell into eight roughly equal volumes, with 5-way and 3-way symmetries. Each shell segment will be filled with electron density. It will be highest at the center of the face of each orbital (as in the traditional hybrid orbital lobe shapes) and will decrease toward the nodal regions between orbitals — as wave structures usually do — where electron density will be lowest (though not zero).

NOTE: Even though it is often useful to talk about these orbitals as separate, they are all — the entire atom is — part of a single, coherent, harmonic, resonant, phase-locked, spherically-symmetrical quantum wave state, and it is all electromagnetic at the root-energy level. Orbitals and their ‘boundaries’ can be seen as nothing more than nodes and antinodes in this harmonic wave structure.

NOTE: The model’s claim is not that an isolated atom always has a definite antinode location in the lab frame. It is that, conditional on one electron being found in a given orbital ‘antinode’ region or direction, the other electrons’ positions must correlated with it in a specific geometric pattern. This conditional-correlation structure is a body-frame feature: it describes the relative positions of electrons within the atom, not their absolute positions in the lab frame. It is the internal frame of reference in which the shell’s wave resonance condition closes and its standing-wave pattern is organized. For a free atom in an unprepared ensemble, all orientations are statistically equivalent so the observed density is typically an orientation average over body-frame orientations, which is observed in the lab frame to be spherically symmetrical.

The diagram below only shows chromium’s eight 3^rd shell p³d⁵-hybrid orbitals. (The darker color represents di-electrons, the lighter color represents unpaired electrons. The sharp edges should not be taken too literally!)

It is also proposed that the stronger repulsion and larger charge density of the three di-electrons will cause them to take up slightly more space and will therefore constrict the five unpaired degenerate electron orbitals slightly. It is expected that this would increase the magnetic signatures of these electrons. (See Magnetic Properties below.)

As in the case of scandium, titanium, and vanadium’, chromiums 3^rd shell p³d⁵-hybrid orbitals exist within the added sheath of the 3s²-orbital di-electron, since it is not needed for hybridization. They are superimposed within it as a harmonic frequency coincides with its fundamental frequency in a resonance. It is proposed that the 3s² di-electron gives additional stability to the electron configuration within it, even though it contains 5 unpaired electrons. The other elements in the d-block will also experience this 3s-orbital stabilization phenomenon, since they achieve at least 4-directional symmetry with only their p– and d-orbitals.

Bonding & Ion Formation

In chromium, a 4s¹-orbital valence shell completes the isolated neutral atom. This is because one of the valence electrons drops down into the 3^rd shell hybridization, achieving 8-directional symmetry. (This occurs in a few other cases, for example copper (Cu) and silver (Ag).)

Removing one electron from the atom gives the free-ion  Cr⁺. When forming a metallic crystal, some of the 4s and 3d electron density delocalizes to form the metallic bond. In both cases, the core electron domain geometry remains the same. (A second ionization, however, would shift its geometry by moving the 2 remaining di-electrons into the axial positions. This assumes that one of the di-electrons will be ionized, rather than an unpaired electron, once again in order to retain 8-directional symmetry.)

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Magnetic Properties

Elemental chromium is (itinerant, incommensurate spin-density-wave) antiferromagnetic below its Néel temperature of about 311 K (38ºC) and is paramagnetic above it. (Its magnetic susceptibility must also be treated as a band response, not as the response of a fixed set of localized atomic moments.)

Chromium has a total of six unpaired electrons, though one of these is a valence electron. In all elements prior to the d-block, unpaired electrons have occurred only in the outer (valence) shell of the atom. Those are the electrons involved in chemical reactions. Chromium is the fourth case of an atom with unpaired ‘core’ valence electrons, and it has five of them, in addition to its single unpaired valence electron. The core electrons are protected from reacting (at least, until chromium becomes a Cr⁺ ion), and they are stabilized by the 3s di-electron ‘fundamental.’ We propose that it is this protection and stabilization of unpaired core electrons that allows them to interact magnetically, and that consequently determines an element’s magnetic properties.

UNPAIRED ‘CORE’ VALENCE ELECTRONS:
While these electrons are technically still valence electrons, which contribute electron density to the crystal electronic band structure in the conduction electron matrix — the 3D electron gas — of the solid metal crystal, some of the 3d electron density remains concentrated around the atomic cores.

PARAMAGNETISM:
In the presence of an external magnetic field, an unpaired ‘core’ valence electron will orient its spin to align with the magnetic field. This will cause the atom to be drawn into and toward that field — via magnetic field cancellation — giving it a positive magnetic susceptibility (χ_m) value. This attractive force is called paramagnetism, and its effects only last as long as the external magnetic field is present. We might therefore presume that, the stronger the paramagnetism, the more ‘unpaired electron character’ is present. Surprisingly, this does not seem to go according the number of unpaired electrons present, as the diagram below illustrates. There must therefore be other contributing factors, which we will investigate below.

When chromium is above its Curie Temperature of 38ºC, it is the third most paramagnetic metal of the 3d row — excluding the ferromagnetic iron, cobalt, and nickel — even though it has the most unpaired core electrons, with five.

As described above, it is proposed that chromium has five unpaired 3^rd shell electrons arranged in a hexagonal bipyramidal electron structure. Due to orbital constriction by the 3 di-electron orbitals in the same shell, the 5 unpaired electron orbitals should be slightly compressed (and concentrated).

The images below are intended to represent the orientation of these electrons in an external (or adjacent atom’s) magnetic field (whose north pole is pointing upwards). (The purple arrows inside the atom represent the 5 unpaired electrons and the black dots represent the relative positions of the 3 di-electrons.)

If we exclude the 4s¹ electron, chromium has five times as many unpaired ‘core’ valence electrons as scandium (with χ_m = +295), yet chromium has a lower magnetic susceptibility value of only χ_m = +167. It is also a lower value than manganese (Mn), which also has five unpaired core electrons but with both of its 4s² electrons. Within the model, this is proposed to involve interactions among its five 3d-derived unpaired electrons. The mechanism that is conjectured here (requiring quantitative calculation) is that this is due to the parallel spin bonding and field cancellation that occurs between its five unpaired electrons, given their proximity, degeneracy, and orbital constriction.

PARAMAGNETIC STRENGTH ANALYSIS:
The following diagram shows the relative paramagnetic strengths of the transition metals, along with their proposed hybrid orbital geometries. (See paramagnetic strength trend analysis for more detail.)

ANTIFERROMAGNETISM:
Elemental chromium is an itinerant, incommensurate spin-density-wave antiferromagnet below its Néel temperature of about 311 K (38°C) and is paramagnetic above it. Its ordered magnetization varies periodically through the crystal and is not adequately described as identical localized moments simply alternating on neighboring atoms.

The spin-density wave is tied to chromium’s band structure and Fermi surface nesting. A Quicycle explanation must reproduce its measured wave vector, temperature dependence, and itinerant character. Pairing of nominal 4s electrons from neighboring atoms may be discussed only as a conjecture requiring quantitative derivation and comparison with the observed spin-density wave.

(NOTE: In this model, regarding electrons, magnetically antiparallel does not mean the same as electrons of opposite spin. The former is a magnetic alignment distinction; the latter is a spin component phase relationship. Electrons of opposite spin can be either magnetically parallel or antiparallel. In the case of Hund’s 2^nd Rule, adjacent degenerate electrons will both align magnetically parallel and will have the same spins, in order to create the lowest energy composite state. [ref]).

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Electrical Properties

It is interesting to note that the three best electrical conductors — silver (Ag), copper (Cu), and gold (Au) — all share a feature with chromium: a single valence s-orbital electron. However, chromium is a much weaker electrical conductor.

We might speculate that such an ‘activated,’ electron-deficient valence conduction band may actually promote the passage of electrical potential. It may simply offer less resistance to it (by having more unoccupied energy states in the band structure that are available to transmit electrons).

What separates the three precious-metal good conductors from chromium is the nature of their core electron resonances. In the three precious metal elements, the inner orbitals are all completely filled with di-electrons, which are diamagnetic. We might speculate then that, upon this ‘non-interfering’ foundation, the single-valence-electron conduction band may support the transmission of electrical potential through the metallic crystal quite effectively. In the case of chromium, however, there are five unpaired electrons on the surface of every atomic core in the crystal. Their magnetic field and spin interactions might interfere with the electrons in the conduction band in such a way that diminishes conductivity, due to resistance. It is further conceivable that, given the ratio of electrons involved, it may decrease chromium’s conductivity to merely one tenth of the conductivity of copper and silver.

That being said, Chromium’s conductivity is determined by its band structure, carrier velocities, scattering rates, defects, temperature, and magnetic order. A rough similarity between a conductivity ratio and an electron-count ratio is not evidence for the proposed mechanism. A quantitative transport calculation is required before relating the domain model to conductivity.

Credence for this conjecture might come from the fact that, even though chromium has a much lower electrical conductivity than copper, it nevertheless has a much higher conductivity than its immediate neighbors in the 3d-block — vanadium (V) and manganese (Mn) — which each have full valence 4s²-orbitals. (Though this fact is not conclusive on its own.)

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OTHER PARAMAGNETIC 3d METALS: Scandium, Titanium, Vanadium, Chromium (also antiferromagnetic), Manganese
FERROMAGNETIC 3d METALS: Iron, Cobalt, Nickel
DIAMAGNETIC 3d METALS: Copper, Zinc